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*> \brief \b ZRZT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
*
* .. Scalar Arguments ..
* INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with ZTZRZF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The original upper trapezoidal M by N matrix A.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is COMPLEX*16 array, dimension (LDA,N)
*> The output of ZTZRZF for input matrix A.
*> The lower triangle is not referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A and AF.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (M)
*> Details of the Householder transformations as returned by
*> ZTZRZF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZRZT01( M, N, A, AF, LDA, TAU, WORK,
$ LWORK )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), AF( LDA, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
DOUBLE PRECISION NORMA
* ..
* .. Local Arrays ..
DOUBLE PRECISION RWORK( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZAXPY, ZLASET, ZUNMRZ
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, MAX
* ..
* .. Executable Statements ..
*
ZRZT01 = ZERO
*
IF( LWORK.LT.M*N+M ) THEN
CALL XERBLA( 'ZRZT01', 8 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
NORMA = ZLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
* Copy upper triangle R
*
CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK,
$ M )
DO 20 J = 1, M
DO 10 I = 1, J
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
20 CONTINUE
*
* R = R * P(1) * ... *P(m)
*
CALL ZUNMRZ( 'Right', 'No tranpose', M, N, M, N-M, AF, LDA, TAU,
$ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
* R = R - A
*
DO 30 I = 1, N
CALL ZAXPY( M, DCMPLX( -ONE ), A( 1, I ), 1,
$ WORK( ( I-1 )*M+1 ), 1 )
30 CONTINUE
*
ZRZT01 = ZLANGE( 'One-norm', M, N, WORK, M, RWORK )
*
ZRZT01 = ZRZT01 / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
IF( NORMA.NE.ZERO )
$ ZRZT01 = ZRZT01 / NORMA
*
RETURN
*
* End of ZRZT01
*
END
|
